In equation REF , the prior \(p(z)\)  is a Gaussian distribution with zero mean and unit variance. To obtain expressive posterior \(q(z|h_t)\) , we use normalizing flows in Partial VAE [1]}. Specifically, we use auto-regressive Neural Spline Flows (NSF) [2]}. Between the two flow layers, we flip the input [3]} and normalize it using ActNorm [4]}. Refer to supp. material for brief overview of NSF. In Figure REF , the flow-based encoder \(S\)  infers the posterior \(q(z|h_t) = S(h_t)\) .
